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Dirac electrons in finite graphene samples with zigzag edges under highmagnetic fields (in the regime of Landau-level formation) are investigated withregard to their bulk-type and edge-type character. We employ tight-bindingcalculations on finite graphene flakes (with various shapes) to determine thesublattice components of the electron density in conjunction with analyticexpressions (via the parabolic cylinder functions) of the relativistic-electronspinors that solve the continuous Dirac-Weyl equation for a semi-infinitegraphene plane. Away from the sample edge, the higher Landau levels are foundto comprise exclusively electrons of bulk-type character (for bothsublattices); near the sample edge, these electrons are described by edge-typestates similar to those familiar from the theory of the integer quantum Halleffect for nonrelativistic electrons. In contrast, the lowest (zero) Landaulevel contains relativistic Dirac electrons of a mixed bulk-edge characterwithout an analog in the nonrelativistic case. It is shown that such mixedbulk-edge states maintain also in the case of a square flake with combinedzigzag and armchair edges. Implications for the many-body correlated-electronbehavior (relating to the fractional quantum Hall effect) in finite graphenesamples are discussed.

Unique nature of the lowest Landau level in finite graphene samples with zigzag edges: Dirac electrons with mixed bulk-edge character